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## Homework Statement

A cannon is supported one meter above the top of a 20 degree declining slope of length 200m. The cannon has a launch velocity of 55m/s. There is a ball halfway down this slope moving at a constant velocity of 20m/s.

-Determine the angle [itex]\Theta[/itex] required for the projectile to hit the bottom of the hill within one degree.

-How long does the projectile take to hit the bottom of the hill?

-There is a target moving at a constant velocity of 20m/s down the hill. How long should you delay firing to hit the target as it reaches the bottom of the hill?

-Find the maximum distance this projectile can travel as measured from the bottom of the hill.

## Homework Equations

x=x[itex]_{0}[/itex]+v[itex]_{0x}[/itex]t

v[itex]_{y}[/itex]=v[itex]_{0y}[/itex]t-gt[itex]^{2}[/itex]

y=y[itex]_{0}[/itex]+v[itex]_{0y}[/itex]t-0.5gt[itex]^{2}[/itex]

v[itex]^{2}_{y}[/itex]=v[itex]^{2}_{0y}[/itex]-2g(y-y[itex]_{0}[/itex])

## The Attempt at a Solution

I have tried using all of the two-dimensional kinematics equations with some success but the problem is that [itex]\Theta[/itex] is unknown so I can't find t or v[itex]_{fy}[/itex].

My best attempts are as so:

v[itex]_{yf}[/itex]=55sin[itex]\Theta[/itex]-9.81t

188=55cos([itex]\Theta[/itex])t

188=0+55cos([itex]\Theta[/itex])t-4.9t[itex]^{2}[/itex]

The diagram for the problem is attached.

Either it is algebra more complicated than I am used to or I am missing something very simple. I am confident that if I could solve for [itex]\Theta[/itex] OR t I could finish the problem easily. I can't seem to get a solveable equation. Thank you for your help and I apologize if there are syntax errors as I am a first time user.

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